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The angle of elevation to a nearby tree from a point on the ground is measured to be 20∘
. How tall is the tree if the point on the ground is 92 feet from the tree? Round your answer to the nearest hundredth of a foot if necessary.

Sagot :

Mhanifaidn

Answer:

  • 33.49 feet

Step-by-step explanation:

This is about the right triangle, where 92 feet side is adjacent leg to 20° angle, x - height.

Use trigonometry to find the height

  • x / 92 = tan 20°
  • x = 92 tan 20°
  • x = 33.49 feet (rounded)

[tex]\\ \rm\rightarrowtail cot\theta=\dfrac{B}{P}[/tex]

[tex]\\ \rm\rightarrowtail cot20=\dfrac{92}{P}[/tex]

[tex]\\ \rm\rightarrowtail P=\dfrac{92}{cot20}[/tex]

[tex]\\ \rm\rightarrowtail P=\dfrac{92}{2.7475}[/tex]

[tex]\\ \rm\rightarrowtail P=33.49ft[/tex]

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